M/G/1之極限機率的尾端行為

Abstract

本文目的在找出進入平穩狀態時 系統中極限分佈的尾巴部分的收斂情形。我們的方法使用嵌入馬可夫鏈的觀念，且我們知道系統中相鄰的兩個離開的人之區段具有相同分佈但不獨立。我們證明相鄰的兩個離開的人之區段有大數法則的性質。接著使用遞迴的方式，我們呈現極限分佈的尾巴部分的下降成一幾何的分佈。藉著我們再拓展它去預測 的結果。

This thesis is to find the behavior of tail limiting distribution of M/G/1 queue in steady-state. Our method includes embedded Markov chain , and in steady state we could know the period between two consecutive custom departure times are identical distribution , but not independent. We prove the series of period between two consecutive custom departure times are adapted to strong law of large numbers. By using the recursive form we show in this paper that the tail of the probabilities decay geometrically as the number of the customers grow large. Next we extend it to guess the behavior of tail limiting distribution of the general M/G/s Queue.